[2sin50+cos10(1+√3tan10)]/√(1+cos10)
=[2sin50+cos10+√3sin10]/√(1+2cos^2 5-1)
=[2sin50+2sin(10+30)]/√(2cos^2 5)
=[2(sin50+sin40)]/(√2*cos5)
=[2(sin50+cos50)]/(√2*cos5)
=[2*√2sin(50+45)]/(√2*cos5)
=[2√2*sin95]/(√2*cos5)
=[2√2*sin(90+5)]/(√2*cos5)
=[2√2*cos5]/(√2*cos5)
=2